Required information
Sheena can row a boat at $2.20 \mathrm{mi} / \mathrm{h}$ in still water. She needs to cross a river that is $1.20 \mathrm{mi}$ wide with a current flowing at $1.60 \mathrm{mi} / \mathrm{h}$. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of $25.0^{\circ}$ from the direction straight across the river.
How long does it take her to cross the river?
minutes

Step 1 ：First, calculate the effective speed of Sheena's boat. This is the speed of the boat in still water minus the speed of the current, because the current is working against her. This will give us the speed at which she is effectively moving across the river. In this case, the effective speed is \(2.20 \mathrm{mi} / \mathrm{h} - 1.60 \mathrm{mi} / \mathrm{h} = 0.60 \mathrm{mi} / \mathrm{h}\).

Step 2 ：Next, consider the angle at which she is heading. If she were heading straight across the river (i.e., at a 90 degree angle to the current), then her effective speed would be the same as the speed we just calculated. However, because she is heading at an angle, her effective speed across the river is less than this. We can calculate her effective speed across the river by multiplying her effective speed by the cosine of the angle at which she is heading. In this case, the effective speed across the river is \(0.60 \mathrm{mi} / \mathrm{h} \times \cos(25.0^\circ) = 0.54 \mathrm{mi} / \mathrm{h}\).

Step 3 ：Finally, calculate the time it takes her to cross the river by dividing the width of the river by her effective speed across the river. In this case, the time is \(1.20 \mathrm{mi} / 0.54 \mathrm{mi} / \mathrm{h} = 2.21 \mathrm{h}\). Convert this time to minutes by multiplying by 60, which gives approximately 132.41 minutes.

Step 4 ：Final Answer: The time it takes for Sheena to cross the river is approximately \(\boxed{132.41}\) minutes.